;;Practice exam:  CMPU 101 - 01 Exam 1 Practice

; 
; Problem 1:
; 
;     Name three types of Racket entities that always evaluate to    
;     themselves and give examples of each of the types. 
;     
;     


; 
; Problem 2:
; 
;    Write a predicate function called SMALL-VALUE? that takes in a  
;    data item (any valid Racket entity) as input and that returns
;    #t if the input is a Boolean value or a number between 0 and 
;    20 (including 0 and 20).  For full credit, your solution 
;    should not use an if or a cond.  If you have trouble writing
;    a solution with no decision statement, try writing the 
;    function with a decision statement first and it might give 
;    you some insight into writing it without if or cond.
;    
;    > (small-value? 7)
;    #t
;    
;    > (small-value? #f) 
;    #t
;    
;    > (small-value? 'foo)
;    #f
;    


;  
; Problem 3: 
;  
;    Design a Scheme function that converts Euros to US 
;    Dollars. Since exchange rates change daily, you should 
;    make your code as readable and maintainable as possible 
;    by using a constant definition for the exchange rate.
; 
;    Be sure to follow the Design Recipe to get full credit for     
;    your solution. 
;    
; 


;  
; Problem 4(a): 
;  
;    Evaluate the following programs (a and b) step by step (as 
;    if you were the Stepper), underlining the portion of the 
;    expression in each step to be evaluated in the next step, 
;    and separating each step with an arrow (->). Circle any 
;    parts of the functions that are not evaluated when the given   
;    function call is made.
; 
;    Function definition:
;    
;    (define my-abs 
;      (lambda (x) 
;        (cond
;          [(> x 0) x] 
;          [(< x 0) (* -1 x)] 
;          [else 0])))
;    
;    Function call:
;    (my-abs (- 4 10))
;    
;    (b):
; 
;    Function definition:
;    
;    (define score 
;      (lambda (x)
;        (cond
;          [(>= x 90) "A"] 
;          [(>= x 80) "B"] 
;          [(>= x 70) "C"] 
;          [(>= x 60) "D"] 
;          [else "F"])))
; 
;    Function call:
;    (score (- 94 20))
; 


; 
; Problem 5:
;  
;     The expression (+ 8 2) evaluates to the value 10.  It is a    
;     compound expression made up of three primitive values. For
;     this problem, write five other Racket expressions whose 
;     values are also the number 10:
;     
;     * A single primitive value.
;     
;     * Another compound expression made up of three primitive
;       values.
;       
;     * A compound expression made up of four primitive values.
;     
;     * A compound expression made up of one primitive value 
;       and two compound subexpressions.
;       
;     * Any other kind of expression.
;  


; 
; Problem 6:
;  
;     Describe what, if anything is wrong with the following       
;     function definitions:
;     
; (a) (define area 
;       (lambda (sqr)
;         (sqr sqr)))
;  
;     Would this definition cause an error?  Why or why not?
;     
; (b) (define func1 
;       (lambda (f (+ 3 x) y)
;         (* x y)))
; 
;     Would this definition cause an error?  Why or why not?
;     
; (c) (define func2 
;       (lambda (z x y z)
;         (* x y)))
; 
;     Would this definition cause an error?  Why or why not?
;     
; (d) (define func3
;       (lambda (z w y x)
;         (add1 x)))
;     
;     Would this definition cause an error?  Why or why not?
;     



; 
; PROBLEM 7:
; 
;   Develop a function called smallest-of-3 that consumes three 
;   numbers and returns the smallest of them.
; 
;   Note:  You are not allowed to use the built-in min function in  
;   your solution, use decision statements instead.
;   


; 
; PROBLEM 8:
; 
;   Develop a function called smart-add that consumes 2 arguments 
;   and adds them.  The trick is that the arguments may be either 
;   numbers (like 18) or strings of digits (like "18").  Your 
;   function should be able to handle both types for either input 
;   argument.
; 
;   HINT: There are 2 parameters in this function, each of which 
;   could be either of 2 types, so you'll need at least 4 examples.  
;   


; 
; PROBLEM 9 (VERSION 1):
; 
;   Develop a function called roman-value that consumes 1 quoted 
;   symbol as an argument and produces a number that is the decimal 
;   version of the given Roman numeral.  You should make sure your 
;   function works for roman numerals up to 1,000 ('i, 'v, 'x, 'l, 
;   'c, 'd, and 'm). If any symbol other than one of the 7 Roman 
;   numerals is entered, you should return the quoted symboln'huh?. 
;   


; 
; PROBLEM 9 (VERSION 2):
; 
;   Rewrite the following function without using the if special 
;   form and without including the literal boolean values #t and     
;   #f in the definition:
;   
;   (define in-range? 
;     (lambda (x) 
;       (if (> x -3)
;           (if (<= x 4) 
;               (if (> x 2)
;                   #t
;                   #f)) 
;           (if (< x -5)
;               #f #t))))
;   
;   


; 
;  PROBLEM 10:
;  
;    Use the method shown in class to convert the following infix    
;    expressions to prefix notation. Do not simplify or remove
;    operators.
;    
;    (a)  (x - 32) * (5/9)
;    
;    
;    (b)  (x + 3y) * (x - y)
;    
;    
;    (c)  4 + 3 * 7 - 5 / (3 + 4) + 6
;    
;    


; 
;  PROBLEM 11:
;  
;    Show the global environment entries created by the following 5 
;    definitions when they are executed in DrRacket:
;    
;       (define U 35) 
;       (define V 17) 
;       (define W (* U V)) 
;       (define X (+ V W)) 
;       (define f (lambda (a b) (+ a (* b 2))))
;       
;       
;    Show the result of typing the name of each entry in the
;    Interactions window.
;       
;       

; 
;  PROBLEM 12:
;  
;    Given particular character sequences (words),indicate 
;    whether the word is a special form, a built-in function, 
;    or neither. 
;    
;    If you answer special form, indicate how the form is
;    evaluated and give an example of a valid use of the form,
;    including the return value (or void if a side-effect 
;    is the only thing returned).
;                               
;    If you answer built-in function, give an example of invoking 
;    the function on valid arguments and indicate the output for
;    your example.
;       
;    If you think the given word is an undefined name, type 
;    "undefined".
;    
;    (a) typo
;    
;    
;    (b) cond
;    
;    
;    (c) string-append
;    
;    
;    (d) my-func
;    
;    
;    (e) begin
;    
;